A fuel-injection arrangement of this kind is disclosed in U.S. Pat. No. 4,846,119. Fuel under pressure is made available to the suction connection of an injection pump by a fuel-feed pump so that the fuel is drawn in by suction free of bubbles during the suction stroke of the injection pump and is pumped in the following injection cycle via the pressure connection and an injection line to the internal combustion engine and is preferably injected into the combustion chamber of the two-stroke engine. For starting the engine, it must be ensured that the pump chamber of the injection pump is filled with fuel so that adequate fuel flows via the injection line to the engine when the pump piston plunges. If the valves mounted in the fuel-injection arrangement leak slightly, then the injection pump as well as the fuel-feed pump can run empty after being at standstill for a longer period of time. The start of the two-stroke engine provided with a fuel-injection arrangement of this kind is then very difficult because no fuel is injected into the combustion chamber notwithstanding the injection pump being actuated. Two-stroke engines of this kind are, as a rule, started with a manually-actuated starting device. The fuel-feed pump will pump fuel only after several start attempts so that the injection pump can take up its work after several strokes without fuel. If pressure-holding valves, suction valves or the like close only incompletely, then the pump action can go toward zero, therefore making a start of the engine impossible.